BELGIUM, DESPITE its venerable history, has been an independent nation an even shorter peroid than the United States. Only 150 years ago, after centuries of shifting back and forth between Spain, Austria, France and the Netherlands, did Dutch-speaking Flanders and French-speaking Wallonia unite to form a single country with the 1,000-year-old city of Brussels as its captital.

An American celebration of the Belgian sesquicentennial opens tonight at 9 with a spectacular fireworks display on the Mall to welcome King Baudouin and Queen Fabiola. They are here to inaugurate "Belgium Today," a two-month festival that will be centered in three American cities and offer a wide-ranging mixture of arts, science, technology, economics and history. Joing Washington in the celebration, New York will open its activities on April 23 and san Francisco on April 25.

The king and queen will be staying at Blair House, but since their visit is an unofficial one their White House reception will be confined to a private lunch with President and Mrs. Carter. Tomorrow morning the king will open a futuristic technology exhibit on the Mall which includes such curiosities as a self-propelling wheel and the world's smallest, computer-cut diamond. The same morning the queen will tour an exhibit at the Phillips Collection devoted to the 20th-century Belgian painter, Leon Spilliaert.

At 6 p.m. tomorrow the king will deliver a keynote address to an invited audience of diplomats and American governmental representatives. Then he and the queen will attend the opening of the Corcoran's extensive George Vantongerloo restrospective, one of the festival's potentially most significant art events. Including numerous works of sculpture and art not previously seen, the show will give art historians a new opportunity to evaluate the position of this Belgian artist who died in 1965 after contributging to several of the century's major artistic trends.

Also included in the king and queen's itinerary is a special double bill at the Smithsonian's Baird Auditorium Tuesday at 6 p.m. featuring the First All Children's Theater of New York and the Flemish Children's Theater of Ghent. On Wednesday the king, who is still recovering from a recent operation, will return with the queen to Belgium. Prince Albert, his brother, and Princess Paola will open the festivities in New York and San Francisco.

In all three cities the emphasis is upon developments that have taken place within the period of Belgian independence. Apart from a medieval exhibit at New York's Pierpont Morgan Library, there are no exhibitions dealing with past splendors such as the works of Rubens, van Dyck, Pieter Brueghel or Hans Memling. Instead, the aim has been to expand understanding of modern Belgium as a complex bilingual culture that has become an economic and political European center. Most of the events are solid and informative, offering quiet revelations and deepening perceptions rather than indulging in the sweeping scale of some previous cultural exchanges such as the "king Tut" exhibit or the Vienna Opera visit.

In part this low-keyed approach is an accurate reflection of Belgium itself, which has tended in modern times to apply more energy to its economy and its cuisine than its esthetic side. The educational thrust is also consistent with the festival's origins in the National Endowment for the Humanities. "Belgium Today" is the fourth in a series of international symposia which NEH initiated in 1977 with a Canadian study funded by a $54,000 grant. The National Endowment for the Arts joined NEH in funding a more ambitious "Mexico Today" in 1978, and in 1979 the two agencies contributed about $250,000 each to help fund "Japan Today."

The $4.5-million budget for "belgium Today" makes it by far the most ambitious of the symposia to date with $2.5 million coming from the Belgian government, $670,000 from NEH, $212,000 from NEA and the rest from corporate and individual contributions here and in Belgium. Both endowments are projecting considerably smaller expenditures for next year's "Egypt Today" and "scandinavia Today" in 1982. NEH Chairman Joseph Duffey, who arrived at the agency after the symposia series had been scheduled, has said that there are no plans for their continuation past 1982.

The most prestigous scholarly event of "Belgium Today" will be this week's Solvay Conference at the National Academy of Sciences. Founded in 1911 by the Belgian chemist Ernest Solway, the conferences are held every three years to discuss problems in chemistry and physics, attracting over the years such notables as Marie Curie and Albert Einstein. Never before held outside Brussels, the conference this year will be chaired by Nobel laureate professor Ilya Prigogine.

For the next two months numerous Washington institutions will be focusing on various aspects of Belgian culture in a barrage of performances, lectures, workshop and discussions. subjects will range from Belgian filmmakers to Belgian economics. Belgian television will also join in the festivities with a special program to be broadcast this Saturday evening from 9 to 11 over public television. The thundering aerial salutes and colorful bursts of tonight's fireworks on the Mall will signal that the Belgian invasion has begun.